What happens to the present value of an annuity when the interest rate rises illustrate?

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Pension annuities are subject to inflation risk

In contrast to the role that interest rates play in lump-sum calculations, pension annuities are not directly impacted by rate changes, said Linda Stone, senior pension fellow at the American Academy of Actuaries. 

Those payments are generally determined by a formula — based on factors such as age, years of service and salary — and are a fixed amount per year.

Higher rates mean a lower lump sum. You are discounting [the value] of a stream of future payments.

Linda Stone

Senior pension fellow at the American Academy of Actuaries

At the same time, to combat inflation, the Federal Reserve last week boosted a key interest rate by 0.75 percentage points, marking the third increase this year and the biggest hike since 1994. Additional upward adjustments are expected.

That's where the connection to pension lump sums comes in. The specific set of IRS-published interest rates — generally based on a corporate bond yield curve — that companies must use in their lump sum calculation has been rising alongside inflation.

"Higher rates mean a lower lump sum," Stone said. "You are discounting [the value] of a stream of future payments."

How interest rates affect lump sum pension payouts

While the IRS updates interest rates monthly, many companies use one month's numbers — say, from August or November — to calculate those one-time payouts for the following year, Stone said.

In other words, a lump sum paid out this year and based on a lower rate set in 2021 would be more than a 2023 payout determined by a higher rate this year.

A simplified illustration: If the rate used is 4%, a pension benefit of $5,000 monthly ($60,000 a year) over 20 years would yield a lump sum of about $815,419, Titus calculated. At 6%, the one-time payout would be about $688,195 — a difference of $127,224 and about 16% lower.

So, if the upward trajectory continues and you're planning to retire with a lump sum in 2023, you could get more if you were to retire this year. 

'Financial wherewithal' needed to manage a lump sum

Of course, interest rates aren't the only factor you should consider when it comes to a one-time payout.

"A lump sum isn't best for everyone," Stone said. "People have to manage that lump sum and make it last their lifetime ... some people have the financial wherewithal to do that, and others don't."

Plus, moving up a retirement date may be easier said than done. It also could mean missing out on income you would have earned in the interim or additional benefit credits you may have earned toward your pension.

Stone's group offers a free program that provides actuary experts to help answer people's questions about their pension plans. However, she said, there may be a raft of other things to consider that go beyond their expertise, i.e., taxes, estate planning, etc.

"There are so many factors that come into play, and people should really talk to a financial advisor before they make a decision, especially if it's a large sum," Stone said.

Present value is the value today of an amount of money in the future. If the appropriate interest rate is 10 percent, then the present value of $100 spent or earned one year from now is $100 divided by 1.10, which is about $91. This simple example illustrates the general truth that the present value of a future amount is less than that actual future amount. If the appropriate interest rate is only 4 percent, then the present value of $100 spent or earned one year from now is $100 divided by 1.04, or about $96. This illustrates the fact that the lower the interest rate, the higher the present value. The present value of $100 spent or earned twenty years from now is, using an interest rate of 10 percent, $100/(1.10)20, or about $15. In other words, the present value of an amount far in the future is a small fraction of the amount.

The fact that a dollar one year from now is less than a dollar today would be true even if the inflation rate were zero. The reason is that we prefer current availability to future availability: we want it now. That is why there is interest even when expected inflation is zero.

The concept of present value is very useful. One can, for example, determine what a lottery prize is really worth. The California state government advertises the worth of one of its lottery prizes as $1 million. But that is not the value of the prize. Instead, the California government promises to pay $50,000 a year for twenty years. If the discount rate is 10 percent and the first payment is received immediately, then the present value of the lottery prize is “only” $468,246.

Present value also helps us with such practical issues as the location of an airport. Suppose someone argues that an airport, say Denver International Airport, should be built twenty miles from the edge of the city because twenty-five years from now the city will have expanded to reach the airport. That means that for twenty-five years, people will spend valuable time going the long distance to and from the airport. The gain is that twenty-five years from now the airport will be appropriately situated. But because the gain from appropriately locating the airport is so far in the future, the present value of this gain is small; therefore, building the airport so far away today probably does not make sense.

About the Author

David R. Henderson is the editor of this encyclopedia. He is a research fellow at Stanford University’s Hoover Institution and an associate professor of economics at the Naval Postgraduate School in Monterey, California. He was formerly a senior economist with President Ronald Reagan’s Council of Economic Advisers.

Further Reading

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